The resistivity size effect refers to the phenomenon by which there is an increase in electrical resistivity with decreasing conductor dimension(s). The resistivity size effect in metals was first observed in 1901, and the basic physics was understood by the mid-twentieth century. However, the phenomenon has seen a recent resurgence of interest as a result of the severe resistivity increase observed in the nanoscale copper (Cu) wires that serve as interconnects in semiconductor device technology.
The resistivity size effect is typically attributed to the momentum loss of carriers along the axis of the conductors due to surface scattering (evidenced by the film-thickness/line-width dependence of resistivity) and grain boundary scattering (evidenced by the grain size dependence of resistivity). The two most widely used physical models for these scattering mechanisms are the Fuchs-Sondheimer (FS) surface scattering model, incorporating a specularity parameter, p, in the range of 0-1 for diffuse vs. specular scattering from surfaces, and the Mayadas-Shatzkes (MS) grain boundary scattering model, incorporating a reflection coefficient, R, in the range of 0-1 for scattering from grain boundaries.